Incomplete contingency tables with censored cells with application to estimating the number of people who inject drugs in Scotland

Estimating the size of hidden or difficult to reach populations is often of interest for economic, sociological or public health reasons. In order to estimate such populations, administrative data lists are often collated to form multi‐list cross‐counts and displayed in the form of an incomplete contingency table. Log‐linear models are typically fitted to such data to obtain an estimate of the total population size by estimating the number of individuals not observed by any of the data‐sources. This approach has been taken to estimate the current number of people who inject drugs (PWID) in Scotland, with the Hepatitis C virus diagnosis database used as one of the data‐sources to identify PWID. However, the Hepatitis C virus diagnosis data‐source does not distinguish between current and former PWID, which, if ignored, will lead to overestimation of the total population size of current PWID. We extend the standard model‐fitting approach to allow for a data‐source, which contains a mixture of target and non‐target individuals (i.e. in this case, current and former PWID). We apply the proposed approach to data for PWID in Scotland in 2003, 2006 and 2009 and compare with the results from standard log‐linear models. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.     

Robust REML estimation for k‐component Poisson mixture with random effects: application to the epilepsy seizure count data and urinary tract infections data

A robust version of residual maximum likelihood estimation for Poisson log‐linear mixed model is developed, and the method is extended to k‐component Poisson mixture with random effects. The method not only provides the robust estimators for the fixed effects and variance component parameters but also gives the robust prediction of random effects. Simulation results show that the proposed method is effective in limiting the impact of outliers under different data contamination schemes. The method is adopted to analyze the epilepsy seizure count data and the urinary tract infections data, which are deemed to contain several potential outliers. The results show that the proposed method provides better goodness of fit to the data and demonstrate the effect of the robust tuning mechanism. Copyright © 2012 John Wiley & Sons, Ltd.     

A population‐based approach to analyzing pulses in time series of hormone data

Studies of reproductive physiology involve rapid sampling protocols that result in time series of hormone concentrations. The signature pattern in these times series is pulses of hormone release. Various statistical models for quantifying the pulsatile release features exist. Currently these models are fitted separately to each individual and the resulting estimates averaged to arrive at post hoc population‐level estimates. When the signal‐to‐noise ratio is small or the time of observation is short (e.g., 6 h), this two‐stage estimation approach can fail. This work extends the single‐subject modelling framework to a population framework similar to what exists for complex pharamacokinetics data. The goal is to leverage information across subjects to more clearly identify pulse locations and improve estimation of other model parameters. This modelling extension has proven difficult because the pulse number and locations are unknown. Here, we show that simultaneously modelling a group of subjects is computationally feasible in a Bayesian framework using a birth–death Markov chain Monte Carlo estimation algorithm. Via simulation, we show that this population‐based approach reduces the false positive and negative pulse detection rates and results in less biased estimates of population‐level parameters of frequency, pulse size, and hormone elimination. We then apply the approach to a reproductive study in healthy women where approximately one‐third of the 21 subjects in the study did not have appropriate fits using the single‐subject fitting approach. Using the population model produced more precise, biologically plausible estimates of all model parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

A log‐linear multidimensional Rasch model for capture–recapture

In this paper, a log‐linear multidimensional Rasch model is proposed for capture–recapture analysis of registration data. In the model, heterogeneity of capture probabilities is taken into account, and registrations are viewed as dichotomously scored indicators of one or more latent variables that can account for correlations among registrations. It is shown how the probability of a generic capture profile is expressed under the log‐linear multidimensional Rasch model and how the parameters of the traditional log‐linear model are derived from those of the log‐linear multidimensional Rasch model. Finally, an application of the model to neural tube defects data is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A multivariate method for meta‐analysis and comparison of diagnostic tests

We present here an extension of the classic bivariate random effects meta‐analysis for the log‐transformed sensitivity and specificity that can be applied for two or more diagnostic tests. The advantage of this method is that a closed‐form expression is derived for the calculation of the within‐studies covariances. The method allows the direct calculation of sensitivity and specificity, as well as, the diagnostic odds ratio, the area under curve and the parameters of the summary receiver operator's characteristic curve, along with the means for a formal comparison of these quantities for different tests. There is no need for individual patient data or the simultaneous evaluation of both diagnostic tests in all studies. The method is simple and fast; it can be extended for several diagnostic tests and can be fitted in nearly all statistical packages. The method was evaluated in simulations and applied in a meta‐analysis for the comparison of anti‐cyclic citrullinated peptide antibody and rheumatoid factor for discriminating patients with rheumatoid arthritis, with encouraging results. Simulations suggest that the method is robust and more powerful compared with the standard bivariate approach that ignores the correlation between tests. Copyright © 2016 John Wiley & Sons, Ltd.     

A unified genetic association test robust to latent population structure for a count phenotype

Confounding caused by latent population structure in genome‐wide association studies has been a big concern despite the success of genome‐wide association studies at identifying genetic variants associated with complex diseases. In particular, because of the growing interest in association mapping using count phenotype data, it would be interesting to develop a testing framework for genetic associations that is immune to population structure when phenotype data consist of count measurements. Here, I propose a solution for testing associations between single nucleotide polymorphisms and a count phenotype in the presence of an arbitrary population structure. I consider a classical range of models for count phenotype data. Under these models, a unified test for genetic associations that protects against confounding was derived. An algorithm was developed to efficiently estimate the parameters that are required to fit the proposed model. I illustrate the proposed approach using simulation studies and an empirical study. Both simulated and real‐data examples suggest that the proposed method successfully corrects population structure.     

Weighted hurdle regression method for joint modeling of cardiovascular events likelihood and rate in the US dialysis population

We propose a new weighted hurdle regression method for modeling count data, with particular interest in modeling cardiovascular events in patients on dialysis. Cardiovascular disease remains one of the leading causes of hospitalization and death in this population. Our aim is to jointly model the relationship/association between covariates and (i) the probability of cardiovascular events, a binary process, and (ii) the rate of events once the realization is positive—when the ‘hurdle’ is crossed—using a zero‐truncated Poisson distribution. When the observation period or follow‐up time, from the start of dialysis, varies among individuals, the estimated probability of positive cardiovascular events during the study period will be biased. Furthermore, when the model contains covariates, then the estimated relationship between the covariates and the probability of cardiovascular events will also be biased. These challenges are addressed with the proposed weighted hurdle regression method. Estimation for the weighted hurdle regression model is a weighted likelihood approach, where standard maximum likelihood estimation can be utilized. The method is illustrated with data from the United States Renal Data System. Simulation studies show the ability of proposed method to successfully adjust for differential follow‐up times and incorporate the effects of covariates in the weighting. Copyright © 2014 John Wiley & Sons, Ltd.     

Patterns of growth in weight and length among American Samoan infants

Well baby clinic records on 1, 186 infants born in 1975 to 1976 on the island of Tutuila, American Samoa, form the basis for this study of the growth in weight and length from birth to 12 months. Semi‐longitudinal curves of weight and length indicate that these infants have median weights near the NCHS 75th percentile (boys) and 90th percentile (girls) up to 6 months, falling to just below the 75th percentile by 12 months. Median lengths are between the NCHS 50th and 25th percentile. Weight gain from birth to six months was found to be higher than for any other reported population (4.92 kg, sexes combined). The infant feeding pattern was found to exert a significant influence on rate of weight gain for boys between birth and 1–4 months, with the breast‐fed boys gaining more rapidly than artificial‐fed infants.     

Distribution‐free models for longitudinal count responses with overdispersion and structural zeros

Overdispersion and structural zeros are two major manifestations of departure from the Poisson assumption when modeling count responses using Poisson log‐linear regression. As noted in a large body of literature, ignoring such departures could yield bias and lead to wrong conclusions. Different approaches have been developed to tackle these two major problems. In this paper, we review available methods for dealing with overdispersion and structural zeros within a longitudinal data setting and propose a distribution‐free modeling approach to address the limitations of these methods by utilizing a new class of functional response models. We illustrate our approach with both simulated and real study data. Copyright © 2012 John Wiley & Sons, Ltd.     

Reliability of data of the Thames cancer registry on 673 cases of colorectal cancer: effect of the registration process.

OBJECTIVE--To measure the reliability of data collected by the Thames cancer registry and to identify factors in the registration process affecting reliability. DESIGN--A retrospective study of data from the registry, including death certificate only registrations, and hospital case notes on cases of colorectal cancer diagnosed in 1983 or 1988. SETTING--Four districts in South Thames region. SUBJECTS--673 cases of colorectal cancer in resident patients. MAIN MEASURES--Dates of birth, diagnosis of cancer, and death; sex; tumour site; whether treatment was given; type of treatment; and district of residence. RESULTS--Among the 416 (62%) case notes retrieved, including 66 death certificate only registrations, full or high agreement between registry data and hospital notes was recorded for sex, district of residence, and dates of birth and death. Only 12% of cases had the same date of diagnosis, which may be due to failure of registry policy. Lower agreement rates occurred for tumour site (87%), whether treatment occurred (84%), and treatments administered (80%, 1983; 72%, 1988). 20% of surgical treatments and 37% of adjuvant therapy, radiotherapy, and chemotherapy were not recorded by the registry. Disagreements were common among death certificate only registrations. Such registrations accounted for 16(32%) disagreements over tumour site, 33(41%) major disagreements over date of diagnosis (difference > 30 days), and 47(44%) disagreements over treatment. In 65 cases the registry failed to capture all treatments carried out within the six month follow up period, 38(58%) of which were for death certificate only registrations. In 36% of death certificate only registrations the patients survived more than one year from diagnosis, indicating a failure of registry policy over retrospective follow up. CONCLUSIONS--Registry data on district of residence; sex; dates of birth, diagnosis, and death are highly reliable, but treatment and tumour site data are less so. Lack of follow up in death certificate only registrations and failure to monitor treatments during follow up period seemed to be associated with disagreements.     

Joint modeling of longitudinal and survival data with missing and left‐censored time‐varying covariates

We propose a joint model for longitudinal and survival data with time‐varying covariates subject to detection limits and intermittent missingness at random. The model is motivated by data from the Multicenter AIDS Cohort Study (MACS), in which HIV+ subjects have viral load and CD4 cell count measured at repeated visits along with survival data. We model the longitudinal component using a normal linear mixed model, modeling the trajectory of CD4 cell count by regressing on viral load, and other covariates. The viral load data are subject to both left censoring because of detection limits (17%) and intermittent missingness (27%). The survival component of the joint model is a Cox model with time‐dependent covariates for death because of AIDS. The longitudinal and survival models are linked using the trajectory function of the linear mixed model. A Bayesian analysis is conducted on the MACS data using the proposed joint model. The proposed method is shown to improve the precision of estimates when compared with alternative methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Individualizing drug dosage with longitudinal data

We propose a two‐step procedure to personalize drug dosage over time under the framework of a log‐linear mixed‐effect model. We model patients' heterogeneity using subject‐specific random effects, which are treated as the realizations of an unspecified stochastic process. We extend the conditional quadratic inference function to estimate both fixed‐effect coefficients and individual random effects on a longitudinal training data sample in the first step and propose an adaptive procedure to estimate new patients' random effects and provide dosage recommendations for new patients in the second step. An advantage of our approach is that we do not impose any distribution assumption on estimating random effects. Moreover, the new approach can accommodate more general time‐varying covariates corresponding to random effects. We show in theory and numerical studies that the proposed method is more efficient compared with existing approaches, especially when covariates are time varying. In addition, a real data example of a clozapine study confirms that our two‐step procedure leads to more accurate drug dosage recommendations. Copyright © 2016 John Wiley & Sons, Ltd.     

Combining stratified and unstratified log‐rank tests in paired survival data

The log‐rank test is the most widely used nonparametric method for testing treatment differences in survival between two treatment groups due to its efficiency under the proportional hazards model. Most previous work on the log‐rank test has assumed that the samples from the two treatment groups are independent. This assumption is not always true. In multi‐center clinical trials, survival times of patients in the same medical center may be correlated due to factors specific to each center. For such data, we can construct both stratified and unstratified log‐rank tests. These two tests turn out to have very different powers for correlated samples. An appropriate linear combination of these two tests may give a more powerful test than either of the individual test. Under a bivariate frailty model, we obtain closed‐form asymptotic local alternative distributions and the correlation coefficient between these two tests. Based on these results we construct an optimal linear combination of the two test statistics to maximize the local power. Simulation studies with Hougaard's model confirm our construction. We also study the robustness of the combined test by simulations. Copyright © 2010 John Wiley & Sons, Ltd.     

Penalized likelihood estimation for semiparametric mixed models,with application to alcohol treatment research

In this article, we implement a practical computational method for various semiparametric mixed effects models, estimating nonlinear functions by penalized splines. We approximate the integration of the penalized likelihood with respect to random effects with the use of adaptive Gaussian quadrature, which we can conveniently implement in SAS procedure NLMIXED. We carry out the selection of smoothing parameters through approximated generalized cross‐validation scores. Our method has two advantages: (1) the estimation is more accurate than the current available quasi‐likelihood method for sparse data, for example, binary data; and (2) it can be used in fitting more sophisticated models. We show the performance of our approach in simulation studies with longitudinal outcomes from three settings: binary, normal data after Box–Cox transformation, and count data with log‐Gamma random effects. We also develop an estimation method for a longitudinal two‐part nonparametric random effects model and apply it to analyze repeated measures of semicontinuous daily drinking records in a randomized controlled trial of topiramate. Copyright © 2012 John Wiley & Sons, Ltd.     

Time‐varying effect modeling with longitudinal data truncated by death: conditional models,interpretations, and inference

Recent studies found that infection‐related hospitalization was associated with increased risk of cardiovascular (CV) events, such as myocardial infarction and stroke in the dialysis population. In this work, we develop time‐varying effects modeling tools in order to examine the CV outcome risk trajectories during the time periods before and after an initial infection‐related hospitalization. For this, we propose partly conditional and fully conditional partially linear generalized varying coefficient models (PL‐GVCMs) for modeling time‐varying effects in longitudinal data with substantial follow‐up truncation by death. Unconditional models that implicitly target an immortal population is not a relevant target of inference in applications involving a population with high mortality, like the dialysis population. A partly conditional model characterizes the outcome trajectory for the dynamic cohort of survivors, where each point in the longitudinal trajectory represents a snapshot of the population relationships among subjects who are alive at that time point. In contrast, a fully conditional approach models the time‐varying effects of the population stratified by the actual time of death, where the mean response characterizes individual trends in each cohort stratum. We compare and contrast partly and fully conditional PL‐GVCMs in our aforementioned application using hospitalization data from the United States Renal Data System. For inference, we develop generalized likelihood ratio tests. Simulation studies examine the efficacy of estimation and inference procedures. Copyright © 2015 John Wiley & Sons, Ltd.     

Incorporating baseline measurements into the analysis of crossover trials with time‐to‐event endpoints

Two‐period two‐treatment (2×2) crossover designs are commonly used in clinical trials. For continuous endpoints, it has been shown that baseline (pretreatment) measurements collected before the start of each treatment period can be useful in improving the power of the analysis. Methods to achieve a corresponding gain for censored time‐to‐event endpoints have not been adequately studied. We propose a method in which censored values are treated as missing data and multiply imputed using prespecified parametric event time models. The event times in each imputed data set are then log‐transformed and analyzed using a linear model suitable for a 2×2 crossover design with continuous endpoints, with the difference in period‐specific baselines included as a covariate. Results obtained from the imputed data sets are synthesized for point and confidence interval estimation of the treatment ratio of geometric mean event times using model averaging in conjunction with Rubin's combination rule. We use simulations to illustrate the favorable operating characteristics of our method relative to two other methods for crossover trials with censored time‐to‐event data, ie, a hierarchical rank test that ignores the baselines and a stratified Cox model that uses each study subject as a stratum and includes period‐specific baselines as a covariate. Application to a real data example is provided.     

Bayesian approach to cancer‐trend analysis using age‐stratified Poisson regression models

Annual Percentage Change (APC) summarizes trends in age‐adjusted cancer rates over short time‐intervals. This measure implicitly assumes linearity of the log‐rates over the intervals in question, which may not be valid, especially for relatively longer time‐intervals. An alternative is the Average Annual Percentage Change (AAPC), which computes a weighted average of APC values over intervals where log‐rates are piece‐wise linear. In this article, we propose a Bayesian approach to calculating APC and AAPC values from age‐adjusted cancer rate data. The procedure involves modeling the corresponding counts using age‐specific Poisson regression models with a log‐link function that contains unknown joinpoints. The slope‐changes at the joinpoints are assumed to have a mixture distribution with point mass at zero and the joinpoints are assumed to be uniformly distributed subject to order‐restrictions. Additionally, the age‐specific intercept parameters are modeled nonparametrically using a Dirichlet process prior. The proposed method can be used to construct Bayesian credible intervals for AAPC using age‐adjusted mortality rates. This provides a significant improvement over the currently available frequentist method, where variance calculations are done conditional on the joinpoint locations. Simulation studies are used to demonstrate the success of the method in capturing trend‐changes. Finally, the proposed method is illustrated using data on prostate cancer incidence. Copyright © 2010 John Wiley & Sons, Ltd.     

Wilms' tumour: a systematic review of risk factors and meta‐analysis

Chu A, Heck JE, Ribeiro KB, Brennan P, Boffetta P, Buffler P, Hung RJ. Wilms' tumour: a systematic review of risk factors and meta‐analysis. Paediatric and Perinatal Epidemiology 2010. Wilms' tumour comprises 95% of all renal cancers among children less than 15 years of age. The purpose of this review is to examine the existing literature on perinatal and environmental risk factors for Wilms' tumour. A search for epidemiological studies that examined risk factors for Wilms' tumour was undertaken in Medline, LILACS, ISI Web of Science and Dissertation Abstracts. A total of 37 studies, including 14 cohort, 21 case–control and 2 case–cohort studies, were identified that examined environmental and perinatal risk factors. Most studies were from Western Europe and North America, and among case–control studies, 16 used randomly selected population‐based controls. We observed a significantly increased risk of Wilms' tumour with maternal exposure to pesticides prior to the child's birth (OR = 1.37 [95% CI 1.09, 1.73]), high birthweight (OR = 1.36 [95% CI 1.12, 1.64]) and preterm birth (OR = 1.44 [95% CI 1.14, 1.81]), although the results regarding pesticide exposure may be subject to publication bias (Egger's test, P = 0.09). Further analyses to adjust for the heterogeneity in the results for high birthweight and preterm birth did not statistically change the significance of the results. Additionally, an increased though not statistically significant risk of Wilms' tumour was associated with maternal hypertension (OR = 1.30 [95% CI 0.99, 1.72]), and, compared with the first born, being a second or later birth was associated with a significantly decreased risk (OR = 0.82 [95% CI 0.71, 0.95]). This review suggests a role for several perinatal and environmental risk factors in the aetiology of Wilms' tumour.     

Analysis of censored discrete longitudinal data: Estimation of mean response

The study of longitudinal data is usually concerned with one or several response variables measured, possibly along with some covariates, at different points in time. In real‐life situations this is often complicated by missing observations due to what we usually refer to as ‘censoring’. In this paper we consider missingness of a monotone kind; subjects that dropout, i.e. are censored, fail to participate in the study at any of the subsequent observation times. Our scientific objective is to make inference about the mean response in a hypothetical population without any dropouts. There are several methods and approaches that address this problem, and we will present two existing methods (the linear‐increments method and the inverse‐probability‐weighting method), as well as propose a new method, based on a discrete Markov process. We examine the performance of the corresponding estimators and compare these with respect to bias and variability. To demonstrate the effectiveness of the approaches in estimating the mean of a response variable, we analyse simulated data of different multistate models with a Markovian structure. Analyses of substantive data from (1) a study of symptoms experienced after a traumatic brain injury, and (2) a study of cognitive function among the elderly, are used as illustrations of the methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Real‐time surveillance for abnormal events: the case of influenza outbreaks

This paper introduces a method of surveillance using deviations from probabilistic forecasts. Realised observations are compared with probabilistic forecasts, and the “deviation” metric is based on low probability events. If an alert is declared, the algorithm continues to monitor until an all‐clear is announced. Specifically, this article addresses the problem of syndromic surveillance for influenza (flu) with the intention of detecting outbreaks, due to new strains of viruses, over and above the normal seasonal pattern. The syndrome is hospital admissions for flu‐like illness, and hence, the data are low counts. In accordance with the count properties of the observations, an integer‐valued autoregressive process is used to model flu occurrences. Monte Carlo evidence suggests the method works well in stylised but somewhat realistic situations. An application to real flu data indicates that the ideas may have promise. The model estimated on a short run of training data did not declare false alarms when used with new observations deemed in control, ex post. The model easily detected the 2009 H1N1 outbreak. Copyright © 2016 John Wiley & Sons, Ltd.